A Lower Bound on the Number of Additions in Monotone Computations

Abstract A computation of rational polynomials that only uses variables, positive rational numbers and the operations addition and multiplication is called a monotone, rational computation. We prove a general lower bound on the minimal number of additions in monotone, rational computations. This lower bound implies that any monotone rational computation of the n th degree convolution at least requires n 2 − 2 n + 1 additions. ( n k )− 1 is the minimal number of additions in any monotone computation of the polynomial that is asociated with the k -clique problem for graphs with n nodes.